Thursday, April 17, 2008

Replacement level: how many wins do injuries cost?

Replacement level can be a bit difficult to define in hockey. Unlike baseball, where Derek Jeter gets hurt and all his playing time goes to a guy who has yet to prove he can hit AAA pitching, an NHL player's minutes get spread around to other NHL players (aka his teammates) while he's hurt. So the Yankees can see the difference between Jeter and true replacement level, while an NHL team might shift every line and give nine low-leverage minutes to a guy who only dresses half the time, obscuring the difference between top players and the 21st guy on the roster.

I'm not going to try to compute replacement level here. Instead, I want to look at how many wins it costs a team when one of their top players is injured. For the last five seasons, I looked at forwards who averaged 19 minutes or more per game and defensemen who averaged 21 minutes or more - and who played between 52 and 74 games with a single team. This roughly corresponds to a team's top two forwards and top two defensemen. I compared their team's record with them in the lineup to its record with them out of the lineup. Here are the results:

The overall winning percentage when players were in the line-up was close to .500 for both datasets, which we would expect since playing time is evenly distributed across good and bad teams. And for both forwards and defensemen, there was a clear difference in winning percentage when these players were out of the lineup. However, the difference was much greater for defensemen overall, and in four out of five seasons for which we have ice time data. Teams can expect to lose four extra games if one of their top two blueliners goes down for the season, while losing a first-line forward appears to cost just one and a half losses. The error bars on these estimates are large, but it's clear that losing a defenseman is a bigger deal than losing a forward.

* - Winning percentage was calculated assuming SO and OT games were ties.

Great analysis on an important question. It does not surprise me that the loss of a top-two defender has a bigger impact than the loss of a top-two defender. On balance hockey has twice as many forwards as defenders. The depth chart for defenders is shorter. Because of this my inutition was that the loss of a top-two defender would have been about twice as damaging as a top-two forward. I confirmed this once with some modeling where I estimated a three point impact for (top) forwards (like your data) but only six points for (top) defensemen (understated relative to your data). Once again, great stuff!

Agreed, good stuff. I did something similar a loooong time ago (20 years), and came away, IIRC, with something like a 25-30 goal difference per 80 games. This was back when there were 7.0-7.5 goals scored per game. I didn't break it down by F/D. Can you show the change in both goals scored and goals allowed? One would hope that we'll see a drop in goals scored for forwards, and perhaps both for defensemen.

Tom - I should check the comments more often...I'll post that data in a few minutes.

Blurt - I watched Game 2 and 4 at the Kilowatt. It would be nice to go to a bar that had seen the light of day this century, but it'll do...I brought the pizza in during the first intermission, if you were there...